E and F are mutually exclusive events. P(E) = 0.1; P(F) = 0.6. Find P(E | F) %3D

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
Problem 3P: Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the...
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**Problem Statement:**

E and F are mutually exclusive events. 
- Probability of Event E, P(E) = 0.1
- Probability of Event F, P(F) = 0.6

Find the conditional probability P(E | F).

**Solution Explanation:**

Since E and F are mutually exclusive events, they cannot occur at the same time. This means that the intersection of E and F is zero, i.e., P(E ∩ F) = 0.

The formula for conditional probability is given by:

\[ P(E | F) = \frac{P(E ∩ F)}{P(F)} \]

Substituting the known values:

\[ P(E | F) = \frac{0}{0.6} = 0 \]

Therefore, the conditional probability P(E | F) is 0.

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Transcribed Image Text:**Problem Statement:** E and F are mutually exclusive events. - Probability of Event E, P(E) = 0.1 - Probability of Event F, P(F) = 0.6 Find the conditional probability P(E | F). **Solution Explanation:** Since E and F are mutually exclusive events, they cannot occur at the same time. This means that the intersection of E and F is zero, i.e., P(E ∩ F) = 0. The formula for conditional probability is given by: \[ P(E | F) = \frac{P(E ∩ F)}{P(F)} \] Substituting the known values: \[ P(E | F) = \frac{0}{0.6} = 0 \] Therefore, the conditional probability P(E | F) is 0. **Interactive Element:** - **Input Box:** An input field is provided for the user to enter their answer. - **Submit Button:** A button labeled "Submit Question" to finalize and check the user's response.
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